Manchester United want to sign Maguire after failing to snap him up from Leicester last summer.
Manchester City are gunning for a deal for 22-year-old Chilwell, and Tottenham are keen on Maddison.
Leicester have lost a host of talent since their 2016 Premier League triumph, with N’Golo Kante and Riyad Mahrez the two major exits.
And new manager Rodgers concedes it will be difficult for the Foxes to retain their top stars – especially with Leicester set to miss out on Europe next season.
Asked about the likes of United bidding again for Maguire, Rodgers said: “They may well come in.
“But it doesn’t worry me.
“I think all you can worry is that you make the team the very best they can be.
“You always have to be prepared for that moment as a club – it happens.
“But at this moment in time, I’m thinking about the team, and making the best that we can.”
Maguire and Chilwell last summer signed big new contracts until 2023 and 2024 respectively.
Maddison also penned a deal until 2023 when he joined from Championship Norwich and is in line for new lucrative terms later this season at the King Power Stadium.
Rodgers is now preparing for Leicester’s first home match under him on Saturday against Fulham in the Premier League.
He lost his opening game in charge at Watford 2-1 to a last-gasp Andre Gray goal.
But there were positive signs at Vicarage Road where Leicester embraced a new three-man central defence with wing-backs.
It helped ball-playing stopper Maguire distribute it using his impressive passing skills.
Rodgers added: “He can step in, but firstly, he can defend.
“He wins his headers, he’s very powerful, he’s brave, he gets blocks in, but the type of game I have always promoted they need to have some comfort on the ball at the back, and he can make passes, so he’s a big talent.”
Rodgers was lured away from Scottish champions Celtic to work with Leicester’s exciting young squad.
They spent £100million last summer on Maddison, Ricardo Pereira, Caglar Soyuncu, Filip Benkovic and Rachid Ghezzal.
But Rodgers expects more cash to strengthen later this year.
Claude Puel’s successor added: “There is no doubt we will look to improve, but there is no figure, no number.
“Each year you have to improve, I’m sure we will spend.”
Rodgers got the nod after talks with director of football Jon Rudkin and Aiyawatt Srivaddhanaprabha, known as Top, who has assumed control after the tragic death of his father Vichai in a helicopter crash.
Rodgers said: “All Top gave me was support.
“For the first time in his life he is without his father, he made this decision without his father.
“He’s been courageous and brave throughout the process, that was clear to see. We will work very closely to give supporters a team they van be proud of.”